Paths of the Planets

In Spring 2004 we will be able to observe several bright planets.
Jupiter and Saturn are well-placed for viewing in the evening sky
throughout the semester, while Mercury will make a brief appearance
at the end of March.
Mars is getting farther away, but is still visible in the western sky,
and Venus is spectacular the whole semester.
We will track Jupiter, Saturn, Mars and Venus to chart their motion
over time.

Background Reading:Stars & Planets, p. 298
to 301 (The Solar System)

As seen from the Earth, the Sun, Moon, and planets all appear to
move along the ecliptic. More
precisely, the ecliptic is the Sun's apparent path among the stars
over the course of a year. (Of course, it's actually the Earth that
moves about the Sun, and not the other way around, but the result of
our orbital motion is that the Sun seems to move against the stellar
backdrop.) The planets don't remain exactly on the ecliptic,
but they stay pretty close to it at all times.

Unlike the Sun, however, the planets don't always move in the same
direction along the ecliptic. They usually move in the same
direction as the Sun, but from time to time they seem to slow down,
stop, and reverse direction! This retrograde motion was
a great puzzle to ancient astronomers. Copernicus gave the correct
explanation: all planets move around the Sun in the same
direction, and retrograde motion is an illusion created when we
observe the other planets from our moving point of view, the planet
Earth.

It's easiest to understand the retrograde motion of Mercury and
Venus. These inner planets are closer to the Sun than we are, and
they orbit the Sun faster than we do. From our point of view, the Sun
moves slowly along the ecliptic (due, of course, to our orbital
motion), while Mercury and Venus run rings around the Sun. So at some
times we see them moving in the same direction as the Sun, while at
other times we see them moving in the opposite direction. For Mars,
Jupiter, Saturn, Uranus, Neptune, and Pluto the explanation is a bit
more subtle. These outer planets are further from the Sun than we
are, and they orbit the Sun more slowly than we do. When the Earth
passes between one of these planets and the Sun, we see it going
backwards because we're moving faster than it is.

When the Earth passes between one of the outer planets and the Sun,
we see the Sun and the planet in opposite parts of the sky; the planet
will rise about the time the Sun sets, remain visible all night, and
set about the time the Sun rises. At this time, the planet is said to
be in opposition to the Sun. Opposition is a good time
to observe an outer planet; it's visible all night, and relatively
close to the Earth.

An outer planet's apparent motion is always retrograde for a
month or two before and after opposition. The length of time when a
planet appears retrograde depends on the planet; it's shortest for
Mars, and generally longest for Pluto. The moment when a planet's
apparent motion changes direction is called a stationary
point, because at that exact instant the planet appears to be
stationary with respect to the stars. An outer planet always has one
stationary point before opposition, and another stationary point after
opposition.

As it turns out, Saturn will be in retrograde
motion at the start of the semester, and will have turned around
and gone back to normal motion by the middle of the semester.
Jupiter's stationary points are on January 4 and May 4, so will be
in retrograde motion the entire time. Mars, at opposition last fall,
is now in direct motion, moving eastward along the ecliptic.

TRACKING PLANETARY POSITIONS

The three charts handed out in class should be used
to plot the positions of Jupiter, Saturn, Mars and Venus. (You can get fresh
copies by following the links below.) These charts show more stars
than you can see with your naked eyes, but under typical urban
conditions most of these stars will be visible with binoculars. Each
chart has a scale of 2 cm per degree; thus, two stars separated
by 0.5° in the sky appear 1 cm apart on these charts. At the
top of each chart is an arrow pointing toward the North celestial pole.

Your assignment is to plot Jupiter and Saturn on their individual charts every
time we observe, and Mars and Venus on their common chart.
This should be pretty routine after a few weeks, and
a reasonably complete set of plotted positions will nicely show the
tracks of all four planets as they move along the ecliptic. Here's how to plot
planetary positions:

Align the chart with the sky by holding it up next to the planet
and turning it until the arrow points toward Polaris.

Center your binoculars on the planet and look at the surrounding
stars. Carefully match the stars you see in your binoculars with
the ones shown on the chart. (Note: the transparent overlay handed
out with the planet charts shows the field of view of the binoculars
- you can use it to help match stars on the chart with those in the
sky.)

Look for patterns of stars which include the planet's present
position. For example, you might notice that the planet is on a
line between two stars, or that the planet and two stars form an
equilateral triangle. You'll get better results if you find two or
more different patterns; each helps you check the other.

After you've matched the stars on the chart with those in the
sky, and found some patterns including the planet, you are ready to
plot the planet's position on your chart. Use a pencil to mark its
position, and compare your chart with the sky a few times to make
sure everything's in the right place.

Once you are satisfied with the position you've plotted, mark
the planet's position with ink. Write the date next to the mark
you've made. (Note: when the planets are near their stationary
points they don't seem to move much, and you may have trouble
indicating which date goes with which mark. One solution is to use
different colors for different observations.)

The point of this exercise is to track the planets over the entire
semester as they switch back from retrograde to normal motion. Don't
worry if we miss a few observations due to bad weather; we can just
pick up again when the weather improves. If you want, you can make
additional observations whenever you have the chance. For example, if
we miss an observation due to bad weather on Tuesday, you can go out
the next clear night and fill in the gap (of course, always write the
current date next to your mark).

REPORT: PATHS OF THE PLANETS

Make the observations described in the section on TRACKING
PLANETARY POSITIONS, and write a report on your results. This report
is due on April 29th (the last class of the semester); if the
weather is good that night, we won't collect the reports until you've
had a chance to make one final observation. Your report should
include, in order,

an introduction explaining the purpose of the observations,

a description of the observing sites and equipment you used,

a summary of your observational results, and

the conclusions you have reached.

In more detail, here are several things you should be sure to do in
your lab report:

Explain retrograde motion in your own terms, and discuss
its significance for early astronomers.

Note any weeks when you found the observations particularly easy
(for example, due to bright stars near a planet's position) or
difficult (due to a lack of bright stars or whatever).

List the last week when each planet was definitely West
of the previous position, and the first week when it was
definitely East of its previous position. (Actually, this only applies
to Saturn, since Mars and Venus are both in direct motion the entire
term, and Jupiter is in retrograde motion the entire time.)

Try to estimate the accuracy of your positions. This is a bit
subjective, but you will probably develop some feeling for your
margin of error as you gain experience. For example, if you think
the positions you plot on these charts are off by less than
0.5 cm, your measurements have an accuracy of 0.25° (since
these charts have a scale of 2 cm per degree).

WEB RESOURCES

These charts show 12.7° by 9.5° regions of the sky. If
printed at a resolution of 100 dpi, the GIF images have an scale
of 2 cm per degree; the Postscript plots should automatically
print at this scale. The faintest stars shown are magnitude 8.5, which is about the
limit for our binoculars from Kapiolani park.

Chart for Venus and Mars: GIF
file or Postscript.
This chart is a full-sky chart, because these planets cross several
constellations during the semester.

REVIEW QUESTIONS

At which time would you expect Venus to show retrograde motion
- when it's between the Earth and the Sun, or when it's on the far
side of the Sun as seen from Earth?

Suppose that we (on Earth) see Mars moving in a retrograde
direction. How would Earth's motion look to an observer on Mars?

It takes Jupiter almost exactly 12 years to complete one orbit
around the Sun. How many times in that 12-year period will an
observer on Earth see Jupiter moving in a retrograde direction?